Hexachord
Encyclopedia
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, a hexachord is a collection of six pitch class
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
es including six-note
Note
In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....
segments of a scale
Musical scale
In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...
or tone row
Tone row
In music, a tone row or note row , also series and set, refers to a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.-History and usage:Tone rows are the basis of...
. The term was adopted in the Middle Ages
Middle Ages
The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...
and adapted in the twentieth-century in Milton Babbitt's
Milton Babbitt
Milton Byron Babbitt was an American composer, music theorist, and teacher. He is particularly noted for his serial and electronic music.-Biography:...
serial theory
Serialism
In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...
.
Middle Ages
The hexachord as a mnemonic device was first described by Guido of ArezzoGuido of Arezzo
Guido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido d'Arezzo was a music theorist of the Medieval era...
, in his Epistola de ignoto cantu and the treatise titled Micrologus. In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
. These six pitches are named ut, re, mi, fa, sol, and la, with the semitone between mi and fa. These six names are derived from the first syllable of each half-line of the 8th century hymn Ut queant laxis
Ut queant laxis
Ut queant laxis or Hymnus in Ioannem are verses in honour of John the Baptist written in Horatian Sapphics by Paulus Diaconus, the eighth century Lombard historian...
.
20th century
Allen ForteAllen Forte
Allen Forte is a music theorist and musicologist. He was born in Portland, Oregon and fought in the Navy at the close of World War II before moving to the East Coast. He is now Battell Professor of Music, Emeritus at Yale University...
in his The Structure of Atonal Music redefines the term hexachord to mean what other theorists (notably Howard Hanson
Howard Hanson
Howard Harold Hanson was an American composer, conductor, educator, music theorist, and champion of American classical music. As director for 40 years of the Eastman School of Music, he built a high-quality school and provided opportunities for commissioning and performing American music...
in his Harmonic Materials of Modern Music: Resources of the Tempered Scale) mean by the term hexad, a six-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row. Carlton Gamer
Carlton Gamer
Carlton Gamer is an American composer and music theorist. He has taught at Princeton University, the University of Michigan, and Colorado College...
uses both terms interchangeably.
Musical cryptogram
A musical cryptogram is a cryptogrammatic sequence of musical notes, a sequence which can be taken to refer to an extra-musical text by some 'logical' relationship, usually between note names and letters. The most common and best known examples result from composers using ciphered versions of their...
on the name of patron Paul Sacher
Paul Sacher
Paul Sacher was a Swiss conductor, patron and impresario.-Biography:He studied under Felix Weingartner, among others. In 1926 he founded the Basel Chamber Orchestra to play works written before the classical period and modern works...
) is notable for its use in multiple compositions including Messagesquisse by Pierre Boulez
Pierre Boulez
Pierre Boulez is a French composer of contemporary classical music, a pianist, and a conductor.-Early years:Boulez was born in Montbrison, Loire, France. As a child he began piano lessons and demonstrated aptitude in both music and mathematics...
.
See also
- Hexatonic scaleHexatonic scaleIn music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole tone scale, C D E F G A C; the augmented scale, C D E G A B C; the Prometheus scale, C D E F A B C; and what some jazz theorists call the "blues scale", C E F F G B...
- Musica fictaMusica fictaMusica ficta was a term used in European music theory from the late 12th century to about 1600 to describe any pitches, whether notated or to be added by performers in accordance with their training, that lie outside the system of musica recta or musica vera as defined by the hexachord system of...
- Guidonian handGuidonian handIn Medieval music, the Guidonian hand was a mnemonic device used to assist singers in learning to sight-sing. Some form of the device may have been used by Guido of Arezzo, a medieval music theorist who wrote a number of treatises, including one instructing singers in sightreading...
- All-interval hexachord
- CombinatorialityCombinatorialityIn music using the twelve tone technique combinatoriality is a quality shared by some twelve-tone tone rows whereby the row and one of its transformations combine to form a pair of aggregates...
- Hexachordal complementationComplement (music)In music the term complement refers to two distinct concepts.In traditional music theory a complement is the interval which, when added to the original interval, spans an octave in total. For example, a major 3rd is the complement of a minor 6th. The complement of any interval is also known as its...
- Mystic chord
- 'Ode-to-Napoleon' hexachord'Ode-to-Napoleon' hexachordIn music, the Ode-to-Napoleon' hexachord is the hexachord named after its use in the twelve-tone piece Ode to Napoleon Buonaparte by Arnold Schoenberg . Containing the pitch-classes 014589 it is labeled 6-20 in Allen Forte's taxonomic system...
- 6-Z446-Z446-Z44 , known as the Schoenberg hexachord, is Arnold Schoenberg's signature hexachord, as one transposition contains the pitches Es, C, H, B, E, G , E, B, and B being Es, H, and B in German....